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Q.

A cube made of an insulating material has uniform charge distribution throughout its volume. Assuming electric potential due to its charge at infinitely distance place to be zero, potential at the center is found $V_{0}$ . What is the electric potential at one of its corners?

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a

$\frac{V_{0}}{8}$

b

$V_{0}$

c

$\frac{V_{0}}{4}$

d

$\frac{V_{0}}{2}$

answer is B.

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Detailed Solution

Question Image
Consider a cube of side ‘2a’ having same charge density as that of cube of side ‘a’.
If ‘V’ is the potential at the corner of a cube of side ‘a’ then potential at the center of cube of side ‘2a’ is given by
$V' = 8 V$
But $V_{0} α \frac{Q}{a}$
   $V' α (\frac{8 Q}{2 a})$
   $∴ \frac{V'}{V_{0}} = 4$
   $∴ V = \frac{V_{0}}{2}$

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